at the moment I have no issues showing one route on a map, but I have no idea how to show multiple routes on the same map...Anyone has already did this with the actions provided with this component?
If yes, can you just explain me the logic that you use?

What you want is to add multiple sets of directions to the same map, displaying at the same time, right? I think that's covered by the component: every directions has a unique Id, so when you add additional ones, they will not clash.

What I want to do is show two diferent routes (or more) with diferents wayponts(specific or each one the routes) that could start on the same orgin point or not. More or less like it's on the attached image.

For example, here's a screenshot displaying two routes between Faro and Porto (stopping in Beja), Lisbon and Madrid (stopping in Badajoz, but passing in other places, such as Toledo) and finally Pamplona and Barcelona (no waypoints). This is the options I used for the second set of Directions: